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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.01596 |
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Table of Contents:
- The $(κ,\ell)$-edge-inducibility problem asks for the maximum number of $κ$-subsets inducing exactly $\ell$ edges that a graph of given order $n$ can have. Using flag algebras and stability approach, we resolve this problem for all sufficiently large $n$ (including a description of all extremal and almost extremal graphs) in eleven new non-trivial cases when $κ\le 7$. We also compute the $F$-inducibility constant (the asymptotically maximum density of induced copies of $F$ in a graph of given order $n$) and obtain some corresponding structure results for three new graphs $F$ with $5$ vertices: the 3-edge star plus an isolated vertex, the 4-cycle plus an isolated vertex, and the 4-cycle with a pendant edge.